Biol 7932, 22 October 2024
2024-10-22
Example: Common Terns (Sterna hirundo) move between colonies (Dittman et. al. 2005, 2007)
Pros:
Limitations
All captured birds (n = 245):
All tagged birds (n = 28):
VHF data:
| Variable | Symbol | Type | Role | Factor Type |
|---|---|---|---|---|
| Returned | R | Binomial | Response | NA |
| Wing chord | WC | Ratio | Explanatory | Fixed |
| Weight | WT | Ratio | Explanatory | Fixed |
Verbal Model: Whether or not a tagged bird returned varies by its weight and wing chord.
R = β0 + βWCWC + βWTWT + βWC x WTWT x WC + ε
df:
(28-1) = (1) + (1) + (1)(1) + 24
morphology_model <- glm(data = banding_data, R ~ weight+wing_chord+weight*wing_chord, family = binomial(link="logit"))
anova(morphology_model)Analysis of Deviance Table
Model: binomial, link: logit
Response: R
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 27 35.165
weight 1 0.06554 26 35.099 0.7979
wing_chord 1 0.34723 25 34.752 0.5557
weight:wing_chord 1 0.60330 24 34.149 0.4373
Call:
aov(formula = morphology_model)
Terms:
weight wing_chord weight:wing_chord Residuals
Sum of Squares 0.014423 0.073559 0.131651 5.887509
Deg. of Freedom 1 1 1 24
Residual standard error: 0.4952907
Estimated effects may be unbalanced
Analysis of Deviance Table
Model: binomial, link: logit
Response: R
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 27 35.165
weight 1 0.06554 26 35.099 0.7979
wing_chord 1 0.34723 25 34.752 0.5557
weight:wing_chord 1 0.60330 24 34.149 0.4373
Our interaction term is not significant, so we can re-write our formal model as:
R = β0 + βWCWC + βWTWT + ε
| Variable | Symbol | Type | Role | Factor Type |
|---|---|---|---|---|
| Returned | R | Binomial | Response | NA |
| Handling Time | HT | Ratio | Explanatory | Fixed |
| Second Handler | HA | Nominal | Explanatory | Random |
Verbal Model: Return status varies by handling time and the second person who handled the bird.
\[ R = \beta_0 + \beta_{HT}HT \]
R = β0 + βHTHT + βHAHA + βHT x HAHT x HA + ε
df:
(28-1) = (1) + (3-1) + (1)(2) + 23
Analysis of Deviance Table
Model: binomial, link: logit
Response: R
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 27 35.165
handling_time 1 0.5688 26 34.596 0.450745
second_handler 2 3.0734 24 31.523 0.215089
handling_time:second_handler 2 12.8555 22 18.667 0.001616 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Call:
glm(formula = R ~ handling_time + second_handler + handling_time *
second_handler, family = binomial(link = "logit"), data = banding_data)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -2.378e+00 2.547e+00 -0.934 0.351
handling_time 5.047e-02 1.230e-01 0.410 0.682
second_handlerHA 7.758e+02 1.256e+05 0.006 0.995
second_handlerSW 3.071e+00 2.566e+01 0.120 0.905
handling_time:second_handlerHA -3.604e+01 5.831e+03 -0.006 0.995
handling_time:second_handlerSW -5.047e-02 1.505e+00 -0.034 0.973
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 35.165 on 27 degrees of freedom
Residual deviance: 18.667 on 22 degrees of freedom
AIC: 30.667
Number of Fisher Scoring iterations: 20
Project supervised by David Wilson
Environment & Climate Change Canada graciously allowed us to use their VHF receivers
Fieldwork help & Photography: Kobe Loveless, Hallie Arno, Sabina Wilhelm, Chris Ward, Gill Holmes
Shout-outs: